logical validity

逻辑有效

Foundations & Logic · Graduate · Mathematics Resources editorial compilation (AI-assisted)

Translation evidence: Literature usage

Meaning in context

A sentence is logically valid if every nonempty structure for its language satisfies it.

语句在其语言的每个非空结构中都为真时称逻辑有效。

Example

∀x  (x=x)\forall x\;(x=x) is valid in logic with equality.

Usage and distinctions

Truth in the intended natural-number structure alone is not validity.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Avigad, Hua, Lewis and van Doorn — Logic and Proof§10.2 Truth in a Model; §10.4 Validity and Logical Consequence; §10.5 Soundness and Completeness · Checked 2026-10-14

Translation sources

  1. 杨睿之（复旦大学）— 数理逻辑，第15讲PDF p.6：⊨α 与「逻辑有效」 · Checked 2026-10-14
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